Mathematical logic hierarchies | Computability theory | Effective descriptive set theory
In mathematical logic, an arithmetical set (or arithmetic set) is a set of natural numbers that can be defined by a formula of first-order Peano arithmetic. The arithmetical sets are classified by the arithmetical hierarchy. The definition can be extended to an arbitrary countable set A (e.g. the set of n-tuples of integers, the set of rational numbers, the set of formulas in some formal language, etc.) by using Gödel numbers to represent elements of the set and declaring a subset of A to be arithmetical if the set of corresponding Gödel numbers is arithmetical. A function is called arithmetically definable if the graph of is an arithmetical set. A real number is called arithmetical if the set of all smaller rational numbers is arithmetical. A complex number is called arithmetical if its real and imaginary parts are both arithmetical. (Wikipedia).
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Determine Sets Given Using Set Notation (Ex 2)
This video provides examples to describing a set given the set notation of a set.
From playlist Sets (Discrete Math)
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
This video introduces the basic vocabulary used in set theory. http://mathispower4u.wordpress.com/
From playlist Sets
Introduction to ADVANCED CALCULUS Sets and Notation
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to ADVANCED CALCULUS Sets and Notation - Definition of a Set and notion/symbols denoting set membership. - Set builder and interval notation. - Definition of union and intersection of sets and set complement. - The set
From playlist Advanced Calculus
Introduction to Set Theory (Discrete Mathematics)
Introduction to Set Theory (Discrete Mathematics) This is a basic introduction to set theory starting from the very beginning. This is typically found near the beginning of a discrete mathematics course in college or at the beginning of other advanced mathematics courses. ***************
From playlist Set Theory
In this video, Tori explains the meaning of a set. She looks into finite versus infinite sets, and explains elements.
From playlist Basics: College Algebra
Determine Sets Given Using Set Notation (Ex 1)
This video provides examples to describing a set given the set notation of a set.
From playlist Sets (Discrete Math)
Spectra in locally symmetric spaces by Alan Reid
PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will
From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)
Regularity and non-standard models of arithmetic #PaCE1
Follow-up video: https://youtu.be/7HKnOOvssvs Discussed text, including all links: https://gist.github.com/Nikolaj-K/101c2712dc832dec4991bf568869abc8 Curt's call: https://youtu.be/V93GQaDtv8w Timestamps: 00:00:00 Introduction 00:02:55 Wittgenstein and predicates (optional) 00:11:12 Skolems
From playlist Logic
Arithmetic regularity, removal, and progressions - Jacob Fox
Title: Marston Morse Lectures Topic: Arithmetic regularity, removal, and progressions Speaker: Jacob Fox Affiliation: Stanford University Date: Oct 25, 2016 For more video, visit http://video.ias.edu
From playlist Mathematics
Arithmetic Mean or Median of Arithmetic Progression (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise
Here's an easier way to find the Mean of Evenly Spaced Numbers. To learn more about Quant- Arithmetic, enrol in our full course now: https://bit.ly/QuantArithmetic In this video, we will learn: 0:00 Arithmetic Mean 0:41 Arithmetic Median 1:16 Arithmetic Mean and Median of evenly spaced
From playlist Arithmetic ( GMAT / GRE / CAT / Bank PO / SSC CGL)
Tom Sanders - Roth's theorem on arithmetic progressions
Roth's theorem on arithmetic progressions
From playlist 28ème Journées Arithmétiques 2013
Chao Li - 2/2 Geometric and Arithmetic Theta Correspondences
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. I will give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also know
From playlist 2022 Summer School on the Langlands program
Negatives numbers from anti msets | Math Foundations 231 | N J Wildberger
How do we set up negative numbers in this new arithmetic based purely on multisets or msets? The answer is surprising: we must adapt notions from 20th century particle physics: the idea of an antiparticle that shares many properties of a particle, but that mutually annihilates when in cont
From playlist Box Arithmetic
Linear equations in smooth numbers - Lilian Matthiesen
Special Year Research Seminar Topic: Linear equations in smooth numbers Speaker: Lilian Matthiesen Affiliation: KTH Royal Institute of Technology Date: October 18, 2022 A number is called y-smooth if all of its prime factors are bounded above by y. The set of y-smooth numbers below x for
From playlist Mathematics
How is i equal to square root of -1?
What is 'i'? More importantly, what is a complex number? How are complex numbers relevant to the context of other familiar numbers? Chapters: 00:00 Introduction 01:46 Logo of Reals and Rationals 02:11 Expanding real numbers 03:25 Motivation using whole (natural) numbers 06:08 Planar numb
From playlist Summer of Math Exposition 2 videos
Maths for Programmers: Sets (What Is A Set?)
We're busy people who learn to code, then practice by building projects for nonprofits. Learn Full-stack JavaScript, build a portfolio, and get great references with our open source community. Join our community at https://freecodecamp.com Follow us on twitter: https://twitter.com/freecod
From playlist Maths for Programmers
The Green - Tao Theorem (Lecture 1) by D. S. Ramana
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020